What it’s for:
Like the t-test, the paired t-test, is used to compare two means, testing the null hypothesis that the two means are equal. The paired t-test is used when the data are collected in pairs, rather than as a random sample within each treatment group. For example, if you wished to test whether a new drug reduced swelling in patients’ legs, you could measure each patient’s leg circumference before and after receiving the drug. Obviously the two measurements on the same patient are not independent, they represent a pair of correlated data. This type of experiment, known as a repeated-measure test, is a common use of the paired t-test.
Assumptions/Cautions:
Data in each treatment group must be normally distributed (parametric test).
Each data point in the first treatment group must be correlated with a single data point in the second treatment group, but independent of all other data points (Zar 1996).
Repeated t-tests cannot be used to compare >2 means. A repeated-measures ANOVA (not desribed in the Science Toolkit) should be used in this situation.
How to use it:
The paired t-test looks at the differences between data points within a pair. We compare the mean of these differences to zero, rather than directly comparing the means of the two samples. If one sample is consistently larger than the other, we would expect a large average difference (which could be positive or negative).
1) Find the number of pairs of data (n).
2) Find the diference (d) between each data pair within sample 1 (X1) and sample 2 (X2). Note: It makes no difference which sample is designated X1, and which is designated X2.
3) Find the mean of these differences.
4) Find the standard error of these differences.
5) Calculate the test statistic (t) by dividing the mean by the standard error, or by using the formula in the box at right (Zar 1996).
6) Calculate degrees of freedom as n – 1 (Zar 1996).
7) Estimate a p-value using your calculated t and df, and a computer program or table.
8) Draw a conclusion, based on the p-value from 3). See also Types of Error.
MS Excel Tips:
MS Excel includes the paired t-test in its Data Analysis Tools (found under TOOLS, DATA ANALYSIS). These tools are included in the version of Excel installed in student computer labs at The University of Lethbridge, but are not included in the default installation of Excel. Custom installation is required. Output of the test includes both the two-tailed and one-tailed p-values, reported as p(T<=t). RETURN